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== Geometry Opener(s) 10/9 10/9 It’s World Post Day!!! Happy Birthday Scotty McCreery, Brandon Routh, Sean Lennon, P.J. Harvey, Guillermo del Toro, Scott Bakula, Tony Shalhoub, Jackson Browne, John Lennon, Yusef Lateef, Aimee Semple McPherson and Camille Saint-Saens!!! 10/9 What to do today: 1. Do the opener. 2. Take notes. 3. Practice using polygon definitions. 4. Use whiteboards. 5. Practice identifying angle pairs. 6. Practice identifying polygon shapes. 7. Work on homework. 8. Do the exit pass. TODAY’S OPENER Agenda 1. Opener (5) 2. Period 1: Lecture/Notes: Definition Decisions (15) 3. Practice: p. 48, #1-11 (Period 6: minus #5-6) (12) 4. Whiteboard practice 1: Some figures to play around with (??) 5. Whiteboard practice 2: Reading the Lesson and Wksht. 1-6, p. 31 (15) 6. HW: Wksht. 1-6, p. 32 & 33 (Period 6: p. 32 in class) (16…Period 1: 1 minute) 7. Exit Pass (5) Essential Question(s) How do I describe polygons? Objective(s) Students will be able to (SWBAT) identify closed versus open polygons. SWBAT identify regular vs. irregular polygons. SWBAT identify simple vs. complex polygons. SWBAT identify concave vs. convex polygons. SWBAT find perimeters of polygons. SWBAT determine polygon side lengths based on perimeter value and # of sides. 1. Two angles are complementary. The measure of one angle is 21 more than twice the measure of the other angle. Find the measures of the angles. Answer? THE LAST OPENER 1. Imagine a big, giant coordinate plane on top of a map of the U.S. A line segment starts at Chicago at (1,-3) and ends at St. Louis at (-12, -13). What is the distance between Chicago and St. Louis? Answer? Exit Pass Connect D, E and F and C to create a polygon. Classify the polygon in terms of the definitions we recorded yesterday and today. The Last Exit Pass ⃗⃗⃗⃗⃗ QP and ⃗⃗⃗⃗⃗ QR are opposite rays, and ⃗⃗⃗⃗⃗ QT bisects RQS. 1. If mRQT = 6x + 5 and mSQT = 7x – 2, find mRQT. 2. If mRQS = 22a – 11 and mRQT = 12a – 8, find mTQS S T R P Q 3. HOMEWORK Period 1 Wksht. 1-6, p. 32. Angle Vocabulary/Algebra quiz on Friday. HOMEWORK Period 6 Same as Period 1. Extra Credit Period 1 Period 6 Stephanie M. (11x) Magda (5x) Prisma (2x) Crystal (4x) Bianca (4x) Jonatan Josie (8x) Alejandra (2x) Stephanie C. Prisma Ayelen (2x) Saul (5x) Michael Yasmin Sandra Refugio Ileanna (2x) Demina Melanie B. (5x) Valerie (9x) Denise (4x) Isaias (2x) Chris Jocelyn Lorenzo (2x) Cynthia (2x) Sergio (8x) Lily (6x) Jasmine Yulissa Edwin (2x) Odalys Carlos Carolina (2x) Melanie G. NOTES: Rays, Angles & Protractors Name Definition 9/24 Figure Notation 2. Angle () An initial point or endpoint with an infinite number of points extending in one direction. 2 rays that share the same endpoint. 3. side Each ray that makes up the angle. Same as a Ray. 4. Degree 1/360th of a full circle. 23° 1. Ray 5. Degree measure How big/small the angle is in degrees. 6. arc 7. Vertex of an 8. Interior of an 9. Exterior of an 10.Right 11.Acute 12.Obtuse 13.Reflex 14.Straight 15.Congruent 16. Bisector What’s new? The curved line inside an angle that distinguishes its interior from its exterior. The endpoint of the two sides of an angle. The inside of an angle, denoted by the arc. (yellow) The outside of an angle, denoted by the ABSENCE of an arc. (green) An angle formed by 2 perpendicular rays, its measure equal to 90° An angle formed by 2 rays, its measure less than 90° An angle formed by 2 rays, its measure greater than 90° An angle formed by 2 rays, its measure greater than 180° An angle formed by 2 opposite rays, its measure equal to 180° 2 angles that have the same degree measure. A ray with an endpoint that is identical to the vertex of an angle and which divides that angle in half ⃖⃗⃗⃗⃗ 𝐼𝐹 BED mABC = 36° A curved line touching the two rays of an angle. A single uppercase printed letter: the middle letter of a named angle. (B in ABC) mABC = 90° mABC < 90° 180 > mABC > 90° 360 > mABC > 180° mABC = 180° ABC ≅ DEF ⃗⃗⃗⃗⃗ BG NOTES: Angle Pairs 9/30 Special Pairs with Special Names Adjacent angles. Vertical angles. Linear pair. below, Polygons A polygon is a plane shape with straight sides. Is it a Polygon? Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). Polygon (straight sides) Not a Polygon (has a curve) Not a Polygon (open, not closed) Polygon comes from Greek. Poly- means "many" and -gon means "angle". Types of Polygons Regular or Irregular If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular Regular Irregular Concave or Convex A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°. If any internal angle is greater than 180° then the polygon is concave. (Think: concave has a "cave" in it) Convex Concave Simple or Complex A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself! Many rules about polygons don't work when it is complex. Simple Polygon (this one's a Pentagon) Complex Polygon (also a Pentagon) More Examples Irregular Hexagon Concave Octagon Complex Polygon (a "star polygon", in this case a pentagram) Names of Polygons If it is a Regular Polygon... Name Sides Shape Interior Angle Triangle (or Trigon) 3 60° Quadrilateral (or Tetragon) 4 90° Pentagon 5 108° Hexagon 6 120° Heptagon (or Septagon) 7 128.571° Octagon 8 135° Nonagon (or Enneagon) 9 140° Decagon 10 144° Hendecagon (or Undecagon) 11 147.273° Dodecagon 12 150° Triskaidecagon 13 152.308° Tetrakaidecagon 14 154.286° Pentadecagon 15 156° Hexakaidecagon 16 157.5° Heptadecagon 17 158.824° Octakaidecagon 18 160° Enneadecagon 19 161.053° Icosagon 20 162° Triacontagon 30 168° Tetracontagon 40 171° Pentacontagon 50 172.8° Hexacontagon 60 174° Heptacontagon 70 174.857° Octacontagon 80 175.5° Enneacontagon 90 176° Hectagon 100 176.4° Chiliagon 1,000 179.64° Myriagon 10,000 179.964° Megagon 1,000,000 ~180° Googolgon 10100 ~180° n-gon n (n-2) × 180° / n You can make names using this method: Sides Start with... Sides ...end with 20 Icosi... +1 ...henagon 30 Triaconta... +2 ...digon 40 Tetraconta... +3 ...trigon 50 Pentaconta... +4 ...tetragon 60 Hexaconta... +5 ...pentagon 70 Heptaconta... +6 ...hexagon 80 Octaconta... +7 ...heptagon 90 Enneaconta... +8 ...octagon 100 Hecta... +9 ...enneagon etc.. Example: a 62-sided polygon is a Hexacontadigon BUT, for polygons with 13 or more sides, it is OK (and easier) to write "13-gon", "14-gon" ... "100gon", etc. Some Figures to Angle Around With Z S W P Y V T R Q X U A B F 4 3 K C 2 B 1 D E J H G